Question

A population is bimodal. A sample of size 39 is taken from this population. The distribution of the sample mean is approximately normal. What "idea" allows us to know this? A. Law of Large Numbers B. Central Limit Theorem C. Properties of probability D. The data is normal because we're told so. Use this information for problems 2 - 4. For the last 20 years, the price that turkey farmers receive for turkeys has been relatively stable (approximately uniformly distributed). In 2018, turkey farmers received an average of µ = 43.3 cents per pound for their birds. Suppose the standard deviation of all prices received by turkey farmers is σ = 7.5 cents per pound. A random sample of 150 turkey farmers in 2018 is one value of many that form the sampling distribution of sample means. What is the mean value for this sampling distribution of sample mean? 3.54 cents per pound 7.5 cents per pound 43.3 cents per pound Not enough information What is the standard error of this sampling distribution of sample mean? 7.5 cents per pound 0.61 cents per pound 3.54 cents per pound Not enough information What is the shape of the sampling distribution of sample mean? Uniform Approximately normal Skewed right Not enough information A national survey by Gallup interviewed 1014 adults and found that they had consumed, on average, 4.2 alcoholic beverages in the past seven days. Considering a sample of 1014 adults was taken, which of the following statements is TRUE? By the central limit theorem, the 1014 weekly number of drinks obtained in the sample is approximately normally distributed. By the central limit theorem, the average weekly number of drinks from repeated samples of size 1014 is approximately normally distributed. By the law of large numbers, the results of this study are 1014 times less variable than if only one U.S. adult had been asked. By the law of large numbers, the average weekly number of drinks from repeated samples of size 1014 is approximately normally distributed. The amount of fill (weight of contents) put into a glass jar of spaghetti sauce has a population mean of 850 g and a population standard deviation of 8 g. Find the probability that a random sample of 14 jars has a mean weight between 848 and 855g. 0.8890 0.3327 Data is not normal; sample size is not large; the CLT does not apply. This can't be done without knowing. Find the probability P(-0.15 ≤ X ≤ 0.4) when X is a normal random variable with mean 0 and standard deviation 1, and the sample size is n = 10. 0.6819 0.8982 Data is not normal; sample size is not large enough; the CLT does not apply. This can't be done without knowing μX and σX. The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ = 6.7 minutes and standard deviation σ = 2.2 minutes. When a sample of 100 is taken, what is the probability that the sample mean is less than 6.4? 0.5542 0.4458 0.9137 0.0863

Name: a population is bimodal a sample of size 39 is taken from this population the distribution of the sample mean is approximately normal what idea allows us to know this a law of large numbers 10432
Uploaded: 2022-09-13T17:05:32-08:00
Duration: 6 min 19 s
Channel: Kari Hasz
Description: a population is bimodal a sample of size 39 is taken from this population the distribution of the sample mean is approximately normal what idea allows us to know this a law of large numbers 10432

Use this information for problems 2 - 4.

For the last 20 years, the price that turkey farmers receive for turkeys has been relatively stable (approximately uniformly distributed). In 2018, turkey farmers received an average of µ = 43.3 cents per pound for their birds. Suppose the standard deviation of all prices received by turkey farmers is σ = 7.5 cents per pound. A random sample of 150 turkey farmers in 2018 is one value of many that form the sampling distribution of sample means.

What is the mean value for this sampling distribution of sample mean?
3.54 cents per pound
7.5 cents per pound
43.3 cents per pound
Not enough information

What is the standard error of this sampling distribution of sample mean?
7.5 cents per pound
0.61 cents per pound
3.54 cents per pound
Not enough information

What is the shape of the sampling distribution of sample mean?
Uniform
Approximately normal
Skewed right
Not enough information

A national survey by Gallup interviewed 1014 adults and found that they had consumed, on average, 4.2 alcoholic beverages in the past seven days. Considering a sample of 1014 adults was taken, which of the following statements is TRUE?

By the central limit theorem, the 1014 weekly number of drinks obtained in the sample is approximately normally distributed.
By the central limit theorem, the average weekly number of drinks from repeated samples of size 1014 is approximately normally distributed.
By the law of large numbers, the results of this study are 1014 times less variable than if only one U.S. adult had been asked.
By the law of large numbers, the average weekly number of drinks from repeated samples of size 1014 is approximately normally distributed.

The amount of fill (weight of contents) put into a glass jar of spaghetti sauce has a population mean of 850 g and a population standard deviation of 8 g. Find the probability that a random sample of 14 jars has a mean weight between 848 and 855g.
0.8890
0.3327
Data is not normal; sample size is not large; the CLT does not apply.
This can't be done without knowing.

Find the probability P(-0.15 ≤ X ≤ 0.4) when X is a normal random variable with mean 0 and standard deviation 1, and the sample size is n = 10.
0.6819
0.8982
Data is not normal; sample size is not large enough; the CLT does not apply.
This can't be done without knowing μX and σX.

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ = 6.7 minutes and standard deviation σ = 2.2 minutes. When a sample of 100 is taken, what is the probability that the sample mean is less than 6.4?
0.5542
0.4458
0.9137
0.0863

Added by Kathleen D.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kari Hasz

09/13/2022

Step 1

Step 1: The idea that allows us to know that the distribution of the sample mean is approximately normal when a sample is taken from a bimodal population is the Central Limit Theorem. Show more…

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A population is bimodal. A sample of size 39 is taken from this population. The distribution of the sample mean is approximately normal. What "idea" allows us to know this? A. Law of Large Numbers B. Central Limit Theorem C. Properties of probability D. The data is normal because we're told so. Use this information for problems 2 - 4. For the last 20 years, the price that turkey farmers receive for turkeys has been relatively stable (approximately uniformly distributed). In 2018, turkey farmers received an average of µ = 43.3 cents per pound for their birds. Suppose the standard deviation of all prices received by turkey farmers is σ = 7.5 cents per pound. A random sample of 150 turkey farmers in 2018 is one value of many that form the sampling distribution of sample means. What is the mean value for this sampling distribution of sample mean? 3.54 cents per pound 7.5 cents per pound 43.3 cents per pound Not enough information What is the standard error of this sampling distribution of sample mean? 7.5 cents per pound 0.61 cents per pound 3.54 cents per pound Not enough information What is the shape of the sampling distribution of sample mean? Uniform Approximately normal Skewed right Not enough information A national survey by Gallup interviewed 1014 adults and found that they had consumed, on average, 4.2 alcoholic beverages in the past seven days. Considering a sample of 1014 adults was taken, which of the following statements is TRUE? By the central limit theorem, the 1014 weekly number of drinks obtained in the sample is approximately normally distributed. By the central limit theorem, the average weekly number of drinks from repeated samples of size 1014 is approximately normally distributed. By the law of large numbers, the results of this study are 1014 times less variable than if only one U.S. adult had been asked. By the law of large numbers, the average weekly number of drinks from repeated samples of size 1014 is approximately normally distributed. The amount of fill (weight of contents) put into a glass jar of spaghetti sauce has a population mean of 850 g and a population standard deviation of 8 g. Find the probability that a random sample of 14 jars has a mean weight between 848 and 855g. 0.8890 0.3327 Data is not normal; sample size is not large; the CLT does not apply. This can't be done without knowing. Find the probability P(-0.15 ≤ X ≤ 0.4) when X is a normal random variable with mean 0 and standard deviation 1, and the sample size is n = 10. 0.6819 0.8982 Data is not normal; sample size is not large enough; the CLT does not apply. This can't be done without knowing μX and σX. The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean μ = 6.7 minutes and standard deviation σ = 2.2 minutes. When a sample of 100 is taken, what is the probability that the sample mean is less than 6.4? 0.5542 0.4458 0.9137 0.0863